Preheat the oven to 350 degrees F. Grease an 8-inch square cake pan.
Sift coconut flour and baking powder together into a bowl.
Combine cocoa powder and butter in a large, microwave-safe bowl. Microwave on high in 30- to 60-second increments, stirring often, until butter melts and mixture is well blended.
Add sugar, eggs, vanilla, and salt to butter mixture; whisk until well combined. Whisk in flour mixture until smooth. Pour batter into the prepared pan and let rest for 10 minutes.
Bake in the preheated oven until a cake tester inserted into the middle comes out clean, 30 to 35 minutes.
Remove from the oven and cool on a wire rack until completely cool, 30 to 45 minutes. Cut into 16 pieces.